Ranging
To estimate a distance between a transmitter and a receiver in a wireless communications network, the transmitter sends a signal to the receiver at a time instant t1 according to a clock of the transmitter. After receiving the signal, the receiver immediately returns a reply signal to the transmitter. The transmitter measures a time of arrival (TOA) of the reply signal at a time t2. An estimate of the distance between the transmitter and the receiver is the time for the signal to make the round trip divided by two and multiplied by the speed of light c, i.e.,
  Distance  =                                                  t            1                    -                      t            2                                      2        ⁢          c      .      This is also known as two-way ‘ranging’.
Ultra Wideband
Ultra wideband signals are drastically different from conventional wireless signals. Not only is the signal spread over a huge frequency range, but the pulses in the signal are also spread out over time. An ultra wideband (UWB) signal is defined as an impulse radio signal with an absolute bandwidth larger than 500 MHz. or a relative bandwidth larger than 20%.
However, as the bandwidth of the UWB signal increases, the signal is less spread in time and a rising edge of the received signal becomes sharper. In precision ranging applications, detecting the arrival time of the rising edge of the received signal at desired accuracies is important. Therefore, it is desired to use UWB signals to provide precise positioning capabilities.
Extremely accurate TOA and position estimation is possible in a single user, line-of-sight (LOS) and single-path environment. However, in a practical setting, multi-path propagation, multi-user interference (MUI) and non-line-of-sight (NLOS) propagation make accurate positioning challenging. When the LOS between a reference node and a target node is blocked, only the reflections of the UWB signal, due to scattering effects, reach the target node. Therefore, the arrival time of the reflected signal does not represent the true TOA. Because the reflected signal travels a longer distance, a positive bias called a NLOS error is included in a measured time delay.
Detection of TOA of a radio frequency (RF) signal is equivalent to the detection of a leading edge of received multi-path components of the signal. Typically, power delay profiles (PDP) of UWB channels are represented by a double exponentially decaying model. On the other hand, individual multi-path components are subject to Nakagami fading. Depending on the environment, the leading edge that is detected may or may not be a sharp edge.
In the prior art, a transmitter sends a signal to a receiver over a wireless radio communications channel. The receiver measures the time of arrival of the received signal. That signal can be described as follows.
As shown in FIG. 3, a symbol waveform 350 includes multiple pulses 360. The waveform is transmitted in a frame interval TF1 310. A next frame 320, which contains no signal, can be an OFF interval. The pulses 360 in the waveform 350 can have positive or negative polarities depending on the information bit to be transmitted. A width 370 of each pulse can be in the order of pico or nanoseconds for ultra-wideband signals. Associated with the symbol is a symbol time TS 330.
As shown in FIG. 4, an alternative symbol waveform includes a single pulse 460, which is transmitted in a frame interval TF2 410 with an associated symbol time TS 430. The transmitted pulse 460 can have a positive or negative polarity depending on the information bit to be conveyed.
FIG. 1 shows a typical prior art communications network with a transmitter 100 and a receiver. The transmitter sends a signal 150 to the receiver.
As shown in FIG. 7, the receiver is a stored-reference or ‘coherent’ receiver 700. The coherent receiver includes a pre-filter 715 and a matched filter 730 serially connected. The pre-filter includes a low noise amplifier (LNA) 710, and a band-pass filter (BPF) 720. Then, in the matched filter, an output of the band-pass filter 720 is multiplied 722 with a template signal 724, which is equivalent to the corresponding transmitted signal waveform 105, and a resulting product is integrated 725. The output of the integrator 725 is entered into a sampling circuitry 735, which samples the output of the integrator to generate discrete observation samples 136 to be used by a time of arrival estimator 750.
Edge detection techniques are applied to the signal returned by the matched filter 730. In the matched filter operation 730, the time shifted template 724 that produces the maximum correlation with the received signal is used, and the highest peak at the output of 736 is considered as the TOA estimate.
The time shift is adaptively adjusted. In other words, correlations of the received signal with shifted versions of a template signal are considered. In a single path channel, the transmitted waveform can be used as an optimal template signal, and conventional correlation-based estimation can be employed. However, in the presence of an unknown multi-path channel, the optimal template signal becomes the received waveform, which is the convolution of the transmitted waveform and the channel impulse response.
Therefore, the correlation of the received signal with the waveform template is suboptimal in a multi-path channel. If that suboptimal technique is employed in a narrowband system, then the correlation peak may not give the true TOA because multiple replicas of the transmitted signal partially overlap due to multi-path propagation.
In order to prevent this effect, super-resolution time delay estimation techniques have been described, M.-A. Pallas and G. Jourdain, “Active high resolution time delay estimation for large BT signals,” IEEE Transactions on Signal Processing, vol. 39, issue 4, pp. 781-788, April 1991. However, those techniques are too complex to perform real time, and requires a large amount of memory.
For some of the matched filter based prior art see: W. Chung and D. Ha, “An accurate ultra wideband (UWB) ranging for precision asset location,” Proc. IEEE Conf. Ultrawideband Syst. Technol. (UWBST), pp. 389-393, November 2003; B. Denis, J. Keignart, and N. Daniele, “Impact of NLOS propagation upon ranging precision in UWB systems,” Proc. IEEE Conf. Ultrawideband Syst. Technol. (UWBST), pp. 379-383, November 2003; and K. Yu and I. Oppermann, “Performance of UWB position estimation based on time-of-arrival measurements,” Proc. IEEE Conf. Ultrawideband Syst. Technol. (UWBST), pp. 400-404, May 2004.
Even though matched filtering is optimum for leading detection technique, it faces practical problems in implementation. Matched filtering requires extremely high sampling rates, which is very difficult for UWB systems.
Because the shapes of pulses can be different at various multi-path arrivals, it is very difficult to match the template pulse of the typically analog correlator to the received shape. Also, it is very difficult to synchronize to each individual multi-path component, which means a loss in the total collected energy. Due to the large bandwidth of the UWB signal, multi-path components are usually resolvable without the use of complex algorithms.
However, the correlation peak at the output of the matched filter will still not necessarily give the true TOA because the first multi-path component is not always the strongest component.
FIG. 8 shows a coherent receiver 800 with a pre-filter process 715 as described above. Here, the output of the pre-filter is provided to a square-law device 810 that takes the square of the input signal and integrates 725 the square. The output of the integrator 725 is sampled 735, and TOA estimation 750 is performed.
The sampling circuit uses a sampling interval of tS, which is equal to a block length TB, The output of the integrator 725 are observation samples z(n), as analytically expressed as:
      z    ⁡          [      n      ]        =            ∑              j        =        1                    N        s              ⁢                  ∫                                            (                              j                -                1                            )                        ⁢                          T              f                                +                                    (                                                c                  j                                +                n                -                1                            )                        ⁢                          T              b                                                                          (                              j                -                1                            )                        ⁢                          T              f                                +                                    (                                                c                  j                                +                n                            )                        ⁢                          T              b                                          ⁢                                                              r              ⁡                              (                t                )                                                          2                ⁢                              ⅆ            t                    .                    